Dynamically change pivots of an object
I found the general solution to "dynamically change any constraint" which subsumes "dynamically change pivot". It's simple: Change the "Influence". 

Flowchart:


Create (stack) as many pivot constraints as required and target them
to the respective objects (or empties). 
Set "Influence" of all the   pivots to "0" before creating any
key-frames. 
For the first rotation about (suppose) the x-axis, key-frame the
x-rotation and set Influence to 1.
Scrub frames till a, rotate as required and key-frame x-rot. 
Now to blend this with the second rotation, scrub a few (k)
frames back till a-k, key-frame the first Pivot's Influence (now
at 1) and also key-frame the second Pivot's Influence (at 0). 
Scrub forward to a+k frame and switch the values of the  first
and second Pivots' Influence; key-frame both. 
Scrub frames and setup the second rotation as before (Step 4.), and so on.


I endorse this method over other simpler Transformation methods since this is parametric and has few dependencies.